8969: Fencing the cows

Little ColdHand wants to build a fence to enclose his cows' grazing area. However, in order for the fence to be effective, it must include all $m$ grass locations. Otherwise, the cows might rebel against him.

To address this issue, Little ColdHand sought assistance from the Interstellar Cow Company. However, the company provided him with only $n$ fence points, and he can only build the fence from a point to another point. The final cost will be the number of points used.

Little ColdHand is aware that the most cost-effective fence would be a convex hull, but he doesn't know the exact number of points required for it. Therefore, he has approached you to help solve this problem:

Determine the minimum number of points needed to construct a fence that completely encloses all $m$ grass-eating locations.

P.S. If the fence intersects any of the grass locations, we do not consider those locations as fully enclosed.

The first line of input contains the integer $T$ ($1\le T\le 10$), the number of test cases. The description of test cases follows.

The first line of each test case contains two integers, $n$ and $m$ ($1\le n\le 500,1\le m\le 500$) — the number of fence points and the number of grass locations.

Each of the next $n$ lines contains the description of fence points. Each line contains two integers ��xi and ��yi (−109≤��,��≤109−109≤xi,yi≤109), describes the fence point ��ai at (��,��xi,yi).

Each of the next $m$ lines contains the description of grass location. Each line contains two integers ��xi and ��yi (−109≤��,��≤109−109≤xi,yi≤109), describes the grass location ��bi at (��,��xi,yi).

it is guaranteed that the sum of $n$ and $m$ over all test cases both do not exceed $4000$.